2m(5m-7)=32

Solution for 2m(5m-7)=32 equation:

2m(5m-7)=32

We move all terms to the left:

2m(5m-7)-(32)=0

We multiply parentheses

10m^2-14m-32=0

a = 10; b = -14; c = -32;
Δ = b2-4ac
Δ = -142-4·10·(-32)
Δ = 1476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{41}}{2*10}=\frac{14-6\sqrt{41}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{41}}{2*10}=\frac{14+6\sqrt{41}}{20}
$